Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.
Generalized Witten Genus and Vanishing Theorems
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abstract
We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of the Witten genus for $8k+2$ dimensional spin manifolds. The Landweber-Stong type vanishing theorems are proven for the generalized Witten genus and the mod 2 Witten genus on string$^c$ and string (generalized) complete intersections in (product of) complex projective spaces respectively.
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Six-dimensional gauge theories and (twisted) generalized cohomology
Combining an abelianized Yang-Mills field with its dual in 6D N=(1,0) supergravity yields a class in twisted K-theory, with the B-field as twist.